• Journal of the Korea Society of Computer and Information
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• v.16 no.6
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• pp.179-186
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• 2011

This paper suggests the minimum number of vertex guards algorithm. Given n rooms, the exact number of minimum vertex guards is proposed. However, only approximation algorithms are presented about the maximum number of vertex guards for polygon and orthogonal polygon without or with holes. Fisk suggests the maximum number of vertex guards for polygon with n vertices as follows. Firstly, you can triangulate with n-2 triangles. Secondly, 3-chromatic vertex coloring of every triangulation of a polygon. Thirdly, place guards at the vertices which have the minority color. This paper presents the minimum number of vertex guards using dominating set. Firstly, you can obtain the visibility graph which is connected all edges if two vertices can be visible each other. Secondly, you can obtain dominating set from visibility graph or visibility matrix. This algorithm applies various art galley problems. As a results, the proposed algorithm is simple and can be obtain the minimum number of vertex guards.

• Journal of the Korea Computer Graphics Society
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• v.4 no.1
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• pp.55-66
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• 1998

This paper presents a simple method for relieving the ambiguity problems within the sub-voxel based surface-fitting approach for the surface construction. ECB algorithm is proposed to avoid the ambiguity problem which is the root of the holes within the resulting polygon based approximation. The basic idea of our disambiguation strategy is the use of a set of predefined modeling primitives (we call SMP) which guarantees the topological consistency of resulted surface polygons. 20 SMPs are derived from the extension of the concept of the elementary modeling primitives in the CB algorithm [3], and fit one to five faces of them to the iso-surface crossing a cell with no further processing. A look-up table which has a surface triangle list is pre-calculated using these 20 SMPs. All of surface triangles in the table are from the faces of SMPs and are stored in the form of edge list on which vertices of each surface triangle are located. The resulted polygon based approximation is unique at every threshold value and its validity is guaranteed without considering the complicated problems such as average of density and postprocessing. ECB algorithm could be free from the need for the time consuming post-processing, which eliminates holes by revisiting every boundary cell. Through three experiments of surface construction from volume data, its capability of hole avoidance is showed.

• Journal of Multimedia Information System
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• v.6 no.1
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• pp.23-30
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• 2019

A communications profile is a system that acquires information from communication links to an ambulance or other vehicle moving on a road and compiles a database based on this information. The equipment (six sets of HDTVs, fish-eye camera, satellite antenna with tracking system, and receiving power from the satellite beacon of the N-star) mounted on the roof of the vehicle, image data were obtained at Yokohama Japan. From these data, the polygon of the building was actually produced and has arranged on the map of the Geographical Survey Institute of a 50 m-mesh. The optical study (relationship between visibility rate and elevation angle) were performed on actual data taken by fish-eye lens, and simulated data by 3D-Map with polygons. There was no big difference. This 3D map system then predicts the communication links that will be available at a given location. For line-of-sight communication, optical analysis allows approximation if the frequency is sufficiently high. For non-line-of-sight communication, previously obtained electric power data can be used as reference information for approximation in certain cases when combined with predicted values calculated based on a 3D map. 3D maps are more effective than 2D maps for landing emergency medical helicopters on public roadways in the event of a disaster. Using advanced imaging technologies, we have produced a semi-automatic creation of a high-precision 3D map at Yokohama Yamashita Park and vicinity and assessed its effectiveness on telecommunications and ambulatory merits.

• Journal of Digital Contents Society
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• v.3 no.2
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• pp.197-209
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• 2002

If we reduce the number of vertexes to decrease bit rate in polygon-based shape coding, the distortion of approximated contour increases rapidly. On the other hand, if we reduce the distortion, the number of vertexes increases rapidly and many bits are required to encode the vertexes. To improve this problem, in this paper we propose the approximation vertex search method. The encoder in the proposed method searches the type of distortion patterns that is the most similar to the shape which polygon edge and contour segment form and then encodes it. And then, the decoder mathematically finds the approximated vertexes from decoded distortion pattern information. Therefore, the proposed algorithm results in encoding many vertexes at a low bit rate and having the smoother shape than conventional method. As shown in computer simulation, the proposed method has less distortion than conventional method. It costs less bit rate by $10{\sim}20%$ than conventional algorithm in same distortion.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1601-1606
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• 1991

We present an algorithm to approximate the Voronoi diagrams of 2D objects bounded by algebraic curves. Since the bisector curve for two algebraic curves of degree d can have a very high algebraic degree of 2 * d$^{4}$, it is very difficult to compute the exact algebraic curve equation of Voronoi edge. Thus, we suggest a simple polygonal approximation method. We first approximate each object by a simple polygon and compute a simplified polygonal Voronoi diagram for the approximating polygons. Finally, we approximate each monotone polygonal chain of Voronoi edges with Bezier cubic curve segments using least-square curve fitting.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1993.04a
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• pp.136-145
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• 1993

This paper considers a reliability problem as a special type of flow problem and presents an algorithm to evaluate the exact 2-terminal reliability of networks by using a backtracking technique. It employs a polygon-to-chain reduction in addition to series and parallel reduction techniques to reduce execution time. In comparisons, it presents a much better performance than other algorithms known to us. We also propose a methodology to apply the algorithm for approximation of the system reliability.

• The Transactions of the Korea Information Processing Society
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• v.3 no.7
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• pp.1753-1762
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• 1996

Since the number of spatial objects go easily into millions, they are stored on a secondary storage. In order to speed up accessing the geometric objects, we investigate spatial database system. The spatial objects are organized and accessed by spatial access methods(SAMs). But, SAMs are not able to organize polygons directly The most popular approach for handing polygon in SAMs is to use MBR apporximaotion as a geometric key. MBR provides a fast but inaccurate answers to approximation-based query processing. The performance of approximation-based spatial query processing depends on which type of approximation is chosen for the spatial objects. A suitable approximation is crucial for reducing the size of the candidate set. The better the approxmation quality, the fewer accesses to the exact object are necessary. In this paper, I proposed a new multicontainer approximation named Slice decomposition. The performance of proposed method is compared with other method.

• International Journal of CAD/CAM
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• v.13 no.1
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• pp.1-11
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• 2013

Just by adjusting the control points iteratively, progressive iterative approximation (PIA) presents an intuitive and straightforward scheme such that the resulting limit curve (surface) can interpolate the original data points. In order to obtain more flexibility, adjusting only a subset of the control points, a new method called local progressive iterative approximation (LPIA) has also been proposed. But to this day, there are two problems about PIA and LPIA: (1) Only an approximation process is discussed, but the accurate convergence curves (surfaces) are not given. (2) In order to obtain an interpolating curve (surface) with high accuracy, recursion computations are needed time after time, which result in a large workload. To overcome these limitations, this paper gives an explicit matrix expression of the control points of the limit curve (surface) by the PIA or LPIA method, and proves that the column vector consisting of the control points of the PIA's limit curve (or surface) can be obtained by multiplying the column vector consisting of the original data points on the left by the inverse matrix of the collocation matrix (or the Kronecker product of the collocation matrices in two direction) of the blending basis at the parametric values chosen by the original data points. Analogously, the control points of the LPIA's limit curve (or surface) can also be calculated by one-step. Furthermore, the $G^1$ joining conditions between two adjacent limit curves obtained from two neighboring data points sets are derived. Finally, a simple LPIA method is given to make the given tangential conditions at the endpoints can be satisfied by the limit curve.

• Journal of Korea Multimedia Society
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• v.5 no.1
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• pp.18-27
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• 2002

A hierarchical representation scheme for planar curves, MBO-tree, is proposed in this paper, which provides natural approximation and efficient localization. MBO-tree is based on the Douglas-Peucker algorithm (iterative end-point fit algorithm), but approximation errors that are stored with corresponding points in MBO-tree nodes and are used for abstraction measures are adjusted by force to eliminate unnatural approximation. The error adjusting is just making the approximation error of a node in a MBO-tree to be less than or equal to that of its parent. In point of localization, the bounding area of a curve is represented with a minimum bounding octangle (MBO), which can enclose the curve more compactly compared with those of other hierarchical schemes, such as the strip tree, the arc tree and the HAL tree. The MBO satisfies the hierarchical inclusion property that is useful for hierarchical geometrical operations, such as the point-inclusion test and the polygon intersection test. Through several experiments, we found that the proposed scheme was able to approximate more naturally and to localize more effectively.

• Journal of the Korean School Mathematics Society
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• v.24 no.2
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• pp.173-190
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• 2021

This study analyzed the proof of the inverse square law, which is said to be the core of Newton's , in relation to the geometric limit. Newton, conscious of the debate over infinitely small, solved the dynamics problem with the traditional Euclid geometry. Newton reduced mechanics to a problem of geometry by expressing force, time, and the degree of inertia orbital deviation as a geometric line segment. Newton was able to take Euclid's geometry to a new level encompassing dynamics, especially by introducing geometric limits such as parabolic approximation, polygon approximation, and the limit of the ratio of the line segments. Based on this analysis, we proposed to use Newton's geometric limit as a tool to show the usefulness of mathematics, and to use it as a means to break the conventional notion that the area of the curve can only be obtained using the definite integral. In addition, to help the desirable use of geometric limits in school mathematics, we suggested the following efforts are required. It is necessary to emphasize the expansion of equivalence in the micro-world, use some questions that lead to use as heuristics, and help to recognize that the approach of ratio is useful for grasping the equivalence of line segments in the micro-world.